Details

Time bar (total: 3.0s)

analyze228.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
75%25%0%5
75%25%0%6
78.1%21.9%0%7
78.1%21.9%0%8
78.1%21.9%0%9
78.1%21.9%0%10
78.1%21.9%0%11
78.1%21.9%0%12
78.1%21.9%0%13
78.1%21.8%0%14

sample56.0ms

Algorithm
intervals
Results
25.0ms49×body2560valid
9.0ms32×body1280valid
7.0ms43×body640valid
4.0ms36×body320valid
3.0ms77×body80valid
2.0ms19×body160valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
05008
15008

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.6b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.9b
(- 1.0 (cos x))
15.0b
(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 41
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
7.0ms
(/ (- 1.0 (cos x)) (* x x))

series9.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
6.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify46.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
04894437
14894437

prune94.0ms

Filtered
34 candidates to 47 candidates (-38.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New361147
Fresh000
Picked101
Done000
Total371148

Merged error: 0.1b

Counts
48 → 11

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (* x x))
0.2b
(/ (cos x) (* x x))
17.3b
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
12×times-frac
11×*-un-lft-identity
7×add-cube-cbrt
6×associate-/l*
5×add-log-exp
4×cbrt-undiv div-exp div-inv difference-of-squares
3×pow1
2×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod distribute-lft-out--
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- sub-div
Counts
3 → 62
Calls
3 calls:
4.0ms
(/ 1.0 (* x x))
4.0ms
(/ (cos x) (* x x))
9.0ms
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

series17.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(/ 1.0 (* x x))
7.0ms
(/ (cos x) (* x x))
7.0ms
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

simplify48.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
04926651
14926651

prune85.0ms

Filtered
50 candidates to 71 candidates (-42.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New70171
Fresh1910
Picked011
Done000
Total711182

Merged error: 0.1b

Counts
82 → 11

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- 1.0 (cos x)) x)
0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
2.9b
(- 1.0 (cos x))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
29×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
9×div-exp
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×associate-/r* div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 113
Calls
3 calls:
6.0ms
(/ (- 1.0 (cos x)) x)
13.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
4.0ms
(- 1.0 (cos x))

series13.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(/ (- 1.0 (cos x)) x)
5.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
3.0ms
(- 1.0 (cos x))

simplify45.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
056581207

prune136.0ms

Filtered
81 candidates to 122 candidates (-50.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1193122
Fresh189
Picked101
Done011
Total12112133

Merged error: 0.1b

Counts
133 → 12

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b
(* x (/ x (- 1.0 (cos x))))
0.1b
(/ x (- 1.0 (cos x)))
0.1b
(/ 1 (* x (/ x (- 1.0 (cos x)))))
2.9b
(- 1.0 (cos x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
42×*-un-lft-identity
34×times-frac
32×add-exp-log
26×add-cube-cbrt
21×associate-*r*
20×add-cbrt-cube
11×div-exp
9×pow1
8×prod-exp distribute-lft-out-- difference-of-squares
6×cbrt-undiv associate-/r* associate-/l* add-log-exp
5×associate-/r/
4×cbrt-unprod
3×rec-exp flip3-- 1-exp associate-*l* flip-- div-inv
2×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num unswap-sqr
1×sub-neg diff-log *-commutative inv-pow
Counts
4 → 123
Calls
4 calls:
9.0ms
(* x (/ x (- 1.0 (cos x))))
7.0ms
(/ x (- 1.0 (cos x)))
8.0ms
(/ 1 (* x (/ x (- 1.0 (cos x)))))
4.0ms
(- 1.0 (cos x))

series23.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(* x (/ x (- 1.0 (cos x))))
7.0ms
(/ x (- 1.0 (cos x)))
5.0ms
(/ 1 (* x (/ x (- 1.0 (cos x)))))
3.0ms
(- 1.0 (cos x))

simplify57.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
060601244

prune113.0ms

Filtered
87 candidates to 135 candidates (-55.2%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1350135
Fresh01010
Picked011
Done011
Total13512147

Merged error: 0.1b

Counts
147 → 12

regimes124.0ms

Accuracy

98.5% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 31.5b

bsearch26.0ms

Steps
ItersRangePoint
6
0.0059693404329976135
0.059391134127186045
0.03386786279469105
10
-1198.0425486802278
-1.229790441104867e-11
-0.03651380642110043

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05343
15343

end0.0ms

sample1.8s

Algorithm
intervals
Results
810.0ms1565×body2560valid
331.0ms1270×body1280valid
255.0ms1511×body640valid
116.0ms909×body320valid
85.0ms2309×body80valid
36.0ms436×body160valid

Profiling

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